Question

What is the equation, In factored form, of the quadratic function shown in the graph?

Answer 1

Given:

The graph of a quadratic function.

To find:

The equation of the quadratic function in factored form.

Solution:

From the given graph it is clear that the graph of the function intersect the x-axis at point (-3,0) and (2,0).

Since -3 and 2 are the zeros of the function, therefore (x+3) and (x-2) are the factors of the required quadratic function.

Now, the function can be written as:

`f(x)=a(x+3)(x-2)` ...(i)

The graph of the function intersect the y-axis at (0,-6). Substituting
`x=0,f(x)=-6` in (i), we get

`-6=a(0+3)(0-2)`

`-6=a(3)(-2)`

`-6=-6a`

`(-6)/(-6)=a`

`1=a`

Substituting
`a=1` in (i), we get

`f(x)=1(x+3)(x-2)`

Therefore, the required function is
`f(x)=1(x+3)(x-2)`.